The Hindu Dr. Bryan Well (unseen), an expert on Indus Valley Civilisation, holding a tablet at The Institute of Mathematical Sciences, Taramani, Chennai. Photo: M. Karunakaran

Combination of `V’ signs and linear strokes were used to indicate volumes

The Indus civilisation had a volumetric system with inscriptions on ceramic vessels (glazed pots from Harappa) indicating that the sign ‘V’ stood for a measure, a long linear stroke equalled 10, two long strokes stood for 20 and a short stroke represented one, according to Bryan Wells, who has been researching the Indus script for more than 20 years.

These markings on the pots are identical to those found on the incised tablets and bas-relief tablets also found in Harappa, said Dr. Wells, who earned his Ph.D. from Harvard University for his thesis on “The Epigraphic Approaches to Indus Writing.” It is to be published as a book in 2010.

Besides, a ceramic vessel from Mohenjo-Daro, which had fragments of blue-coloured bangles inside, had one long stroke and seven short strokes inscribed on it. When these broken pieces were reconstructed with a computer, they turned out to be 17 bangles. This again established that one long stroke equalled 10 and each short stroke one, Dr. Wells said. He described the findings as “an important discovery” and “very interesting.”

Dr. Wells has proposed that “these sign sequences [sign ‘V’ plus numerals] are various values in the Indus volumetric system. The bas-relief tablets might have been used as ration chits or a form of pseudo-money with the repetitive use of ‘V’ paired with ||, |||, |||| relating to various values in the Indus volumetric system. The larger the ceramic vessel, the more strokes it has. This postulation can be tested by detailed measurements of whole ceramic vessels with clear inscriptions.”

For instance, he recently measured the volume of the three pots from Harappa, which are now with the Archaeological Survey of India (ASI) at Purana Quila in New Delhi. While the smallest of them had three long strokes and a ‘V’ sign, the bigger one had six long strokes and a ‘V’ sign and the biggest seven long strokes and a scale inscribed below it. When he measured their volumes, Dr. Wells found that the pot with three long strokes had an estimated volume of 27.30 litres, the vessel with six long strokes 55.56 litres and the one with seven 65.89 litres. Thus, the calculated value of one long stroke was 9.24 or approximately 10 litres.

Dr. Wells (58), who is now a Senior Researcher in the Institute of Mathematical Sciences, Taramani here, has also focussed on creating an adequate sign list and corpus for the Indus script and the structural analysis of the Indus texts.

He said he first saw the pictures of these pots with markings in the “Corpus of Indus Seals and Inscriptions,” edited by Asko Parpola and his colleagues. When he learnt that the pots were with the ASI at Purana Quila, Dr. Wells travelled there to measure their volumes.

No coincidence

It was Michael Jansen, another researcher on Indus civilisation, who discovered the pot with broken bangles at Mohenjo-Daro in 1987. What intrigued Dr. Wells was the text of one long stroke and seven short strokes inscribed on it. When he reconstructed these broken pieces, using their internal circumferences, with a computer, he found that 17 bangles must have remained intact inside. Besides, the rake sign in the Indus script had a value of hundred and the double rake sign, 200. “This is completely regular” and “not a result of coincidence,” he said. When the ‘V’ sign with linear strokes that occurred on the Harappan tablets were found repeated on a number of ceramic vessels, “it gave me the idea that the ‘V’ sign is probably a measure,” Dr. Wells explained.

It was possible that wages were paid in grain (from these vessels) dispersed from a centralised storage facility, or in the case of incised tablets, material for construction projects and other short-term projects was distributed. He asserted that “there is archaeological evidence bearing on this issue in the form of standardised ceramics with texts describing their contents.”

“Fish” for weights

Dr. Wells agreed with another Indus scholar Steve Bonta’s (Pennsylvania State University) theory that the “fish” sign in the script stood for weights. According to Dr. Bonta, the fish sign occurred frequently with numbers in the script and in clusters too. He later found that the Akkadian Sargonic texts referred to the weight systems of Dilmun (Bahrain) as “minus.” The system of weights from Dilmun was exactly the same as that of the Indus system. Dr. Bonta, who speaks Tamil, realised that “min” in Tamil meant fish. “So our theory is that the term “minus” is derived from the Indus and that the fish are weights,” Dr. Wells said. There were fish signs with one long stroke, two long strokes, a single rake or a double rake. “So the sign graph is doubling and the value is doubling. I think this is too much of a coincidence. But I am aware that a lot of people will disagree with me on the fish sign,” he added.

Combination of ‘V’ signs and linear strokes were used to indicate volumes

— Photo credits: Bryan Wells (Above) The three pots from Harappa with volumetric inscriptions on them. Calculations indicate that the Indus volumetric system is based on multiples of 9.24 litres. (Below) A reconstruction of broken bangles from the Moneer area of Mohenjo-Daro. The number of reconstructed bangles (17) matches the number from the sealing text on the pot that had the broken bangles inside. The other photo shows Indus fish signs.

CHENNAI: The Indus civilisation had a volumetric system with inscriptions on ceramic vessels (glazed pots from Harappa) indicating that the sign ‘V’ stood for a measure, a long linear stroke equalled 10, two long strokes stood for 20 and a short stroke represented one, according to Bryan Wells, who has been researching the Indus script for more than 20 years.

These markings on the pots are identical to those found on the incised tablets and bas-relief tablets also found in Harappa, said Dr. Wells, who earned his Ph.D. from Harvard University for his thesis on “The Epigraphic Approaches to Indus Writing.” It is to be published as a book in 2010.

Besides, a ceramic vessel from Mohenjo-Daro, which had fragments of blue-coloured bangles inside, had one long stroke and seven short strokes inscribed on it. When these broken pieces were reconstructed with a computer, they turned out to be 17 bangles. This again established that one long stroke equalled 10 and each short stroke one, Dr. Wells said. He described the findings as “an important discovery” and “very interesting.”

Dr. Wells has proposed that “these sign sequences [sign ‘V’ plus numerals] are various values in the Indus volumetric system. The bas-relief tablets might have been used as ration chits or a form of pseudo-money with the repetitive use of ‘V’ paired with ||, |||, |||| relating to various values in the Indus volumetric system. The larger the ceramic vessel, the more strokes it has. This postulation can be tested by detailed measurements of whole ceramic vessels with clear inscriptions.”

For instance, he recently measured the volume of the three pots from Harappa, which are now with the Archaeological Survey of India (ASI) at Purana Quila in New Delhi. While the smallest of them had three long strokes and a ‘V’ sign, the bigger one had six long strokes and a ‘V’ sign and the biggest seven long strokes and a scale inscribed below it. When he measured their volumes, Dr. Wells found that the pot with three long strokes had an estimated volume of 27.30 litres, the vessel with six long strokes 55.56 litres and the one with seven 65.89 litres. Thus, the calculated value of one long stroke was 9.24 or approximately 10 litres.

Dr. Wells (58), who is now a Senior Researcher in the Institute of Mathematical Sciences, Taramani here, has also focussed on creating an adequate sign list and corpus for the Indus script and the structural analysis of the Indus texts.

He said he first saw the pictures of these pots with markings in the “Corpus of Indus Seals and Inscriptions,” edited by Asko Parpola and his colleagues. When he learnt that the pots were with the ASI at Purana Quila, Dr. Wells travelled there to measure their volumes.

No coincidence

It was Michael Jansen, another researcher on Indus civilisation, who discovered the pot with broken bangles at Mohenjo-Daro in 1987. What intrigued Dr. Wells was the text of one long stroke and seven short strokes inscribed on it. When he reconstructed these broken pieces, using their internal circumferences, with a computer, he found that 17 bangles must have remained intact inside. Besides, the rake sign in the Indus script had a value of hundred and the double rake sign, 200. “This is completely regular” and “not a result of coincidence,” he said. When the ‘V’ sign with linear strokes that occurred on the Harappan tablets were found repeated on a number of ceramic vessels, “it gave me the idea that the ‘V’ sign is probably a measure,” Dr. Wells explained.

It was possible that wages were paid in grain (from these vessels) dispersed from a centralised storage facility, or in the case of incised tablets, material for construction projects and other short-term projects was distributed. He asserted that “there is archaeological evidence bearing on this issue in the form of standardised ceramics with texts describing their contents.”

“Fish” for weights

Dr. Wells agreed with another Indus scholar Steve Bonta’s (Pennsylvania State University) theory that the “fish” sign in the script stood for weights. According to Dr. Bonta, the fish sign occurred frequently with numbers in the script and in clusters too. He later found that the Akkadian Sargonic texts referred to the weight systems of Dilmun (Bahrain) as “minus.” The system of weights from Dilmun was exactly the same as that of the Indus system. Dr. Bonta, who speaks Tamil, realised that “min” in Tamil meant fish. “So our theory is that the term “minus” is derived from the Indus and that the fish are weights,” Dr. Wells said. There were fish signs with one long stroke, two long strokes, a single rake or a double rake. “So the sign graph is doubling and the value is doubling. I think this is too much of a coincidence. But I am aware that a lot of people will disagree with me on the fish sign,” he added.

6 Responses to “Indus civilisation reveals its volumetric system!”

My response to the above, sent to the concerned scholars:
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“With my due respect to the scholars, as an ordinary man from Chennai with some knowledge of mathematics and Indus symbology, I would like to get clarification on the following points from the learned scholars – Dr Brian wells and Steve Bonta hailing from great Universities. Incidentally, I had opportunity to listen to Michael Witzel when he was with Brian wells in Chennai:

1. If the symbols V paired with l ll lll , etc., represent numbers in terms of 10 or so, such interpretation should be applicable and proven according for all such symbols, wherever, they occur. Whether it is done or not?

2. The same lll with cap, ll/, l//, and other symbol combinations are there! How would they correlate with such analysis?

4. Moreover, such strokes have in one row, two rows and three rows also. Did computer say something?

5. Small strokes are available with long strokes. Why then the computer analysis did not say that it is 1½, 1¼ , ¾ ⅛ etc?

6. If “fish” sign in the script stood for weights, as he agrees with Steve Bonta, then the hypotheses of Asko Parpola (ஒருமீன், இருமீன் etc) and Iravatham Mahadevan (bearer in Tamil) have to be discarded. Or they have to respond to this type of interpretation.

7. To arrive at the conclusion that “one long stroke” was 9.24 and thus should represent 10 litres approximately, three examples have been given. 3 = 37.30, 6 = 55.56 and 7 = 65.89. Whether such mathematics could work with all such strokes without deviation?

8. Why litres, why not kgs or some other unit?

9. Even the man symbol is shown with carrying such strokes in his / her hands! Does it means, he / she carries 30 litres, 40 litres etc, with single hand? [Still I do not know as to why the great Indus deciphers have not identified the “man” symbol is man, woman or otherwise]

10. Such symbols have been found on other things also other than ceramic vessels. Why then the analysis is restricted to ceramic vessels, long strokes found on them, that too only chosen ones?
After all, the computer would give results according our programming.

Therefore, the scholars who always claim that they decipher the Indus script / pictograms or read in a particular language via., Tamil, Arabic etc., they should come out boldly with concrete evidence not piecemeal picking five or ten symbols here and there and coming to a conclusion and forcing on Indians, particularly, the wonderful racist “Dravidians” who jump immediately and proceed with fantastic, fascinating and amazing interpretations and conclusions excelling the discoverers and inventors themselves!

If it indicates a ‘volumetric system’, we can go one step further and even claim that they were describing a four-dimensional world a la Einstein and Minkowski. (See Raum and Zeit by Hermann Minkowski.) There is no end to such fantasy.

All this is speculation. It is part of a campaign to assign the Harappan civilization to the imaginary ‘Dravidians’ and keep alive the Aryan myth. See Kim Plofsker’s Mathematics in India to see how they are trying to use even mathematics to introduce the Aryan invasion through the backdoor.

My next book will put an end to all this. The late Jha and I held back our results becasue we knew that the Witzel-Farmer duo and their camp followers would lauch hysterical diversionary attacks to save their Aryan and foreign origins of the Vedas theories. Now that they are in disgrace and IE Studies is headed for the dustbin of history, we can hopefully expect a saner climate.

Indus numerals are related to Brahmi numerals as are the signs. These people are trying to read Roman numerals into Indus signs!

If sets of long strokes indicate tens and sets of short strokes indicate ones, how does one explain the sets of twelve short strokes? Why do the sets of long strokes never number 8 or higher? Why is 10 (shorts) so exceedingly rare and 11 (long, short, or stacked) nonexistent? Why are 1 and 2 (long and short) found hundreds of times while 6 shorts appear a mere handful of times and 6 longs never show up on seals? The frequency data (see Korvink 2007) are extremely odd, any way you slice it, dice it, or analyze it.

Examination of the corpus of actual inscriptions reveals more oddities. 3 longs show up next to 3 longs (inscription 4444). What does the sequence 1 short + 8 stacked + 2 long mean (2697)? Why are so many shorts and longs occasionally paired? Whatever can 3 shorts + 3 shorts + 3 shorts mean (4402)? And what about 7 shorts + 4 shorts (2799)? One of the oddest is this: D with slash (bow & arrow?) + long 1 + short 2 + short 1 + stacked 5 (7035). Since there are both symbols for 9 shorts and 9 stacked, why didn’t they just add all these together?

“Word” order also varies in a way not found in natural language. 3717 shows 2 stacked upside-down U shapes (double medj) followed by 3 shorts. 2800 shows 4 shorts followed by 4 stacked medj. And so on.

Whether the Harappans spoke a Dravidian language, an Indo-Iranian language, a Munda language, or even Etruscan, these are all extremely odd facts. Simply labeling the Harappan script “proto-Brahmi” does not even begin to explain any of these peculiarities.

1. Deciphering, identifying and showing certain signs / strokes etc as numerals and proceeding to analyse and establish its number system, actual working of mathematics with place value etc.

2. Deciphering, identifying and showing certain signs / symbols / pictograms / strokes etc in combination proceeding to analyze and show that such combunation has been a language written in such script and all the available seals / inscriptions could be read exactly in that particular language without any deviation, compromise or imposed conditions based on one’s own assumptions and presumptions.

In both cases, scholars have been selective in their picking up certain seals, read accordng to their pre-determined “evovled ideas” in their minds, interpret according to suit their hypotheses and theories.

We can have “Steve farmers” in the western world, as we have “Madhivanans” here in India. In research methdology, decoding and decipherment of IVC seals forgetting or purposely keeping the culture, tradition, heritage and civilization of their authors in isolation cannot make it successful and acceptable to all.

The “Aryan-Dravidian” interpretation do not help, as the so-called “Sangam literature” or the ancient literature of “Dravidians” help “Aryans” than “Dravidians”. Unfortnately, most of the western scholars thrive on their attempted decipherment without sufficient knowledge of ancient Tamil tradition, heritage and civilization.

Learning from the books , Indian friends etc., would not be enough qualification to interpret like “masters”, as Michael Witzel got exposed in Chennai!

The books have been written with racial bias, professional prejudice etc., thus leading to no conclusion, in spite of their excellent scholarship, professional acumen and archaeological expertise.

Though now I am unable to comment on this issue I have discovered a tally mark rock plate from a megalithic site in the border of Kerala and Tamilnadu.. It is engraved on rock and look almost same as that marked in the pots. It is about 4 ft. long , but more could have been. Unfortunately rest of the area is broken off from forest fire. If some body likes to see the photographs send a mail.